DE10340793A1 - Processed time sequence measurement data systematic error detection procedure for meteorological or other data uses autocovariance processing of additive white noise - Google Patents

Abstract

A processed time sequence measurement data systematic error detection procedure modulates the data before processing with a definite reproducible white noise signal from a random number generator seed whose amplitude corresponds to the statistical error so that after processing an autocovariance analysis of small time intervals gives the systematic errors in the final result.

Description

The The invention relates to a method for mathematical determination of systematic Errors as part of a work with data processing routines Processing of measured data experimentally obtained in time series.

at the data processing of experimentally obtained measurement data time series is the specification of an error for the calculated data is an essential basis for discussion the Results. In metrology is generally between statistical and systematic errors. While a statistical error using statistical methods, especially the autocovariance method and spectral analysis, determined directly from the calculated time series requires consideration of systematic errors, for example, by the calibration accuracy of the used Sensors are given, an explicit error calculation. Vary the values of measurands during a Observation period noticeable, so is the error in the end result a likewise time-dependent Size. A So error consideration should be for different time intervals may be possible along the measurement period.

at the error calculation in connection with the determination of systematic Errors are so far applied essentially two methods, namely the Error propagation calculation and the so-called Monte Carlo method.

The classical error propagation calculation is an analytical solution of the Problems and is based on the linearization of the calculation routines in terms of their input quantities Formation of local derivatives according to the respective measured variable. she so can for every combination of the input quantities and errors is calculated explicitly become. requirement for the implementation this method is that the local Ablei tion can be formed, the data processing follows a functional context.

at The error propagation method has the disadvantage that in the Linearization by formation of the local derivative already one first source of error because in highly nonlinear relationships and huge Error amplitudes significant deviations arise. This known Method considered also no possible sign dependence (asymmetry) in the Error propagation. The effect of a correlation, so one functional relationship between different error contributions, is also not covered by this known method.

aggravating requires implementation an error calculation according to the known error propagation method a considerable programming effort, since virtually the entire Data processing process are simulated in the error calculation and permanently to the respective state by appropriate extensions must be adjusted. The error calculation in the classical sense is So a program module that is larger in size than to interpret the one of the actual data processing process is. In those cases, where the data processing is a non-functional relationship follows, is the calculation of an error propagation at all not possible.

Monte Carlo method are based on a specific combination of measured values of a time series, e.g. Mean values, applied. They are based on the random, artificial Variation of one of the measured quantities at the input the processing with subsequent Processing of this combination of values. This data processing is done so often to a statistically rele vant statement about the error in the result can be taken.

The Known Monte Carlo method is based on a repeated calculation the data with varying input parameters. It must be a statistical relevant number of calculations carried out become meaningful Result can be achieved. This requires an extremely high Computing or time consuming what this type of error calculation for fast Analyzes rather uninteresting or sometimes even completely unsuitable. Also, the result of the error calculation applies only to this one affected Place in the time series. A comprehensive error analysis thus requires a corresponding procedure at different times along of the time series, which of course still takes the time and effort of computation once considerably enlarged.

There the data processing of time series data partly very can make complex, as an example here the meteorological aircraft measurement is called a classic error propagation calculation in the form of an analytical solution, those based on the linearization of the processing routines through use a local derivative, in such a case because of complicated relationships, the large number of measured variables used and the scope of the processing routines usually no longer feasible. But also the Monte Carlo methods are usually more systematic for error calculation To rule out mistakes because they are one to achieve a meaningful result require high computing and time.

Of the Invention is based on the object, an error detection method for systematic errors to create time series measurement data, the comprehensive error consideration even with complex calculations in the data processing of time series allows. The process to be created by the invention should be low Expenditure to be applicable to all data processing routines and thereby systematic dependencies the output error and the temporal changes of the measured quantities as well to consider their mistakes.

According to the invention, which relates to a method of the type mentioned, is solves this problem in an advantageous and expedient manner in that the measured data before their processing a defined white noise signal whose amplitude is the underlying statistical Error corresponds to the variability of the data signal by applying the Autocovariance method is separable, that with the noise signal modulated measurement data time series by means of the intended data processing routines in unchanged Be processed way that after processing by means of Autocovariance analysis of the amount of white noise that is evident propagated the processed time series into the processing result has, within a small time interval at any point is analyzed in the data and immediately the amount of systematic Error in the final result delivers.

advantageous and appropriate training and embodiments of the method according to the invention are in the dependent claims specified, directly or indirectly, to the claim referred back are.

The comprehensive and complete Error calculation is made possible according to the invention thereby that on the experimentally obtained measured data time series a defined Noise signal is modulated whose amplitude is the underlying corresponds to statistical error. This can be done in an advantageous way be reached using a random generator, as he did as a standard routine is available to most programming languages or from the manuals can be copied to the appropriate languages. requirement for this advantageous method is that this noise function by using a so-called seed value defined and reproducible displayed is.

The generated in this way noise signal is completely uncorrelated and recorded evenly all Frequencies of the spectrum. Because of these characteristics, this is white noise also very easy to separate from the real variability of the measured data signal. Two methods are commonly used namely to one the spectral analysis and the other the autocovariance method. Because of the simpler realization is in the process according to the Invention uses the autocovariance method. In the autocovariance method the variance is shown by white noise as a sharp peak with the time deviation dt = 0, whereas the real measured data signal variability as continuous Curve underneath.

At the Method according to the invention, the error calculation is done by Processing the thus prepared by the modulated noise signal Measurement data time series. The bill is therefore identical to the actual one Data processing. Thus, you can all data processing routines are used unchanged. To Successful processing is carried out by means of an autocovariance analysis the amount of white Noise, resulting from the processed time series in the result has propagated within a small time interval at any point analyzed in the data. This amount of noise is immediate the amount of the systematic error in the final result.

By Choice of identical seed values for Different measurement parameters can be used when generating the error signal for this Sizes correlated signal can be modulated at any amplitude. This allows the analysis of such correlated errors. It is also possible to have one to use variable error amplitude, e.g. assuming a relative Error, and to evaluate in a processing step.

The Method according to the invention has a number of advantages, the following in comparison with the already existing methods error propagation and the Monte Carlo method.

in the Comparison with the two mentioned known methods can be The method according to the invention is very easy to implement and demand only a small program cost. It only requires the preparation the time series at the beginning of the bill and an evaluation at the end. The actual data processing routines are used unchanged. Generators for white Noise is a typical component of any processing software and the determination of the white Noise with the help of autocovariance is a common and accepted Method.

In addition, the method according to the invention requires only a very low computational effort compared to the two mentioned known methods, since only one run is required in the data processing. After this run is a mistake viewing for all sizes and times without further program runs possible.

The Nature of the method according to the invention allows it in contrast to the two mentioned known Methods, error consideration at any point in the data processing program, also for Intermediate sizes, without to carry out further effort.

Different as with the two known methods, by using defined seed values in the generation of the noise signal correlations between different Errors in the error calculation are considered. The usage the seed values allow it over addition, to remove the noise modulation from the measurement data again, without having to read in the measurement data again. This allows the return in the normal data processing without added noise signal. The targeted Switching on and off of the noise contribution allowed for certain measured variables furthermore, the specific error contribution from these sources to investigate and quantify.

in the Contrary to the known error propagation method is the error calculation method according to the invention completely independently from the complexity the data processing routines. It also takes into account non-functional relationships in data processing, e.g. in the scaling of measured values by interpolation of calibration values.

in the Comparison with the known error propagation method is the Method according to the invention exactly and comes without approximations or restrictive Assumptions. It takes into account it also changes automatically on the processing code and does not need to be adapted to the data processing become.

At the Method according to the invention In the first step, the modulation of a measurement data time series takes place by a random signal. For this, the error modulation on the actual measured data signals added, wherein the measured data signal is not recorded during the modulation. This mixes the given, real varying course of the measured variable with the stochastic error signal.

With However, thanks to the autocovariance method, these contributions are easily available To separate the final result. In contrast, the works known error propagation method not with the modulation of Measurements and the well-known Monte Carlo method is over a Modulation of isolated averages operated.

At the Method according to the invention takes place in the second step, a one-time Processing of the measurement data record. The procedure allows an error calculation to realize with only one processing run. This is only because of this possible because superimposed on a noise signal and the real time variation of a measured variable become. As a result, the method according to the invention is extremely fast. at the known error propagation method, however, are along the Time series Any number of bills to record the time course a mistake needed. Even with the use of the known Monte Carlo method many calculation runs are required until the statistics reasonably meaningful.

At the Method according to the invention, the interaction of all sources of error be examined simultaneously in all processing parameters. By simultaneous application of the noise signal to all input variables the integral effect of all sources of error at any time immediately clearly visible. If not by using identical noise waveforms over the Seed values of a random number generator can be adjusted among themselves desired correlations of the error sources are generated unfold the single errors completely independently from each other their effect. The end result thus shows at all times the uncertainty from the overlay independent Sources of error. The known error propagation method, however, shows the effect of all mistakes only for each one final size separately. In the known Monte Carlo method, only one output variable is always modulated and it is applied only to a representative value combination, e.g. Mean values, ie only at one time of the measurement.

The working according to the invention Procedure allows an error calculation for all intermediate processing sizes. The white Noise contained in the output quantities is, of course, turns up every point in the data processing, including the intermediate sizes, as an overlay the contributions from the processed sizes. Thus, an analysis of the noise contribution is at each point in the program (time and measurand) possible. at the known error propagation method, on the other hand, is an explicit one bill for each calculated size and for each time necessary. In the known Monte Carlo method, the error calculation is only for a certain Value combination (time) performed.

The method according to the invention also allows an analysis of the effects of correlated error sources. By using identical seed values, the error time series can be accurately reproduced to be modulated with, for example, a different sign or different amplitude of a different output. This is especially necessary when zwi There is a functional connection between the sources of error of two different quantities. In the known error propagation method, a correlation between different measured variables can not be taken into account at all, since in this case only a mean error amplitude is calculated. Even when using the known Monte Carlo method, the interaction of various error sources is not representable, since only one size is varied.

The Method according to the invention will be described in detail below explained by drawings. Show it:

1 in a block diagram the known existing Messdatenverarbeitung without error calculation,

2 in a block diagram of a measured data processing, which is extended by an operating according to the method according to the invention error calculation,

3 for example, in a time chart, a time series of flight measurement data, namely, the calculated outside temperature, calculated from original measurements (below in FIG 3 ) and measured values with white noise superimposed (top in 3 ), and

4 in a time chart over a small time interval autocovariances of the same time series, wherein the original measured values time series is white lifting within the noise-staggered time series shown in black line.

In 1 is shown in a block diagram schematically a common existing measurement data processing, for example, for the meteorological flight measurement, but no error calculation of systematic errors is provided. The measurement data are in a time series by means of a detection device 1 detected and in a data processing device 2 processed using processing routines. The calculated values, eg the outside temperature values prevailing during the time series, are then displayed in a result output device 3 output.

The data processing of the flight measurement data relating to the example is very expensive. The data processing routines used in the present case comprise, for example, about 20,000 program lines. Approximately 60 measured variables are included in the data processing and the number of calculated secondary data and intermediate quantities used in the data processing device 2 is about 50, with the length of the time series typically being 150,000 values. A complete error calculation is in such an application, even in international comparison, not yet common, since on the basis of the previously known and previously extensively acknowledged error calculation methods of the corresponding effort was not justifiable.

2 shows in comparison with 1 at which points of the measured data processing an extension of the data processing process realizing the method according to the invention is undertaken. The measurement data acquisition device will be taken over unchanged from the existing measurement data processing 1 and the data processing device executing the processing routines 2 , The error calculation requires an intervention only in front of the data processing device 2 in the form of a first program module 4 performing the modulating of the white noise on the measurement data and the data processing device 2 in the form of a second program module 5 that evaluates the noise component in the end result. In order to perform the error analysis at different times of a measurement data time series, only the last step, namely the autocovariance analysis, in the program module 5 repeated. In the program module 5 the choice of a small time interval [t0 - dt, t0 + dt] is made, for which an autocovariance analysis is carried out. In the result output device 3 Finally, the result of all calculated values is output with errors at the respective time t0.

3 shows the effect of white noise on a measured data time series using the example of a calculated quantity. Shown here is the static temperature of the free atmosphere along the flight path of a meteorological research aircraft. In addition to the actual temperature measurement on the sensor, many other variables are included in the calculation of this variable, such as the back pressure, the static pressure, aerodynamic variables from the differential pressures of a flow probe or the like, which all show a characteristic error.

3 In the upper function diagram shows the effect of all these errors on the final result, which is shown in the lower function representation without this error contribution for comparison.

In detail is in 3 a time series (time t in sec) of flight measurement data, namely the calculated outside temperature T in ° K, calculated from original measured values (below) and measured values with superimposed white noise (top) functionally represented. The noise term in the final result shown above appears in the upper illustration of 3 However, it can be seen from this representation that the absolute value of the calculated outside temperature T is still the same.

In 4 Autocovariances AKV of the same time series are shown in a selected small time interval, the original measured value time series being located white in contrast within the noise-staggered time series, which is shown with a black line. It can be seen that the original variance / shape of the time series can be separated from the contribution of white noise by autocovariance.

4 shows that with the help of the autocovariance method the atmospheric variance can be separated from the white noise without any problems, so the original structure of the measured data signal is available as separate information. The sharp peak S in the autocovariance AKV at dt = 0 of the time deviation axis dt yields, after subtracting the real subsurface U (= natural variance of the measured data time series), directly the variance V of the systematic result error resulting from the errors of the calculated output variables and thus their individual variance contributions.

1

detector

2

Data processing device

3

Result output device

4, 5

Program modules

AKV

autocovariance

dt

Time interval time deviation axis in sec

S

top

t

Time in sec

T

outside temperature in ° K

U

Underground; natural Variance of the time series

V

variance the systematic result error

Claims (10)

Method for the computational determination of systematic errors in the context of working with data processing routines processing in time series experimentally obtained measurement data, characterized in that the measurement data before their processing a defined white noise signal is modulated whose amplitude corresponds to the underlying statistical error and that of the variability of the data signal is separable by application of the autocovariance method that the measured data time series modulated with the noise signal are processed by the intended data processing routines in the same way that after completion of the processing by autocovariance analysis of the amount of white noise propagated from the processed time series in the processing result has, within a small time interval, analyzed anywhere in the data and immediately yields the amount of systematic error in the end result. Method according to claim 1, characterized in that that the defined white Noise signal is derived from a random generator whose generated Noise functions defined by using one seed each and reproducible representable. Method according to claim 2, characterized in that that for different measurement parameters noise functions with different Seed values are selected for modulation of input measurement data and be applied simultaneously, so that individual errors completely independent of each other to unfold their effect. Method according to claim 2, characterized in that that for different measurement parameters Noise functions with identical seed values selected for modulation of input measurement data and applied simultaneously become, so that the integral effect of all errors and their Develop correlation immediately at any time. Method according to claim 4, characterized in that that as a noise signal for different measurement parameters a correlated signal of any amplitude is modulated. Method according to claim 4, characterized in that that as a noise signal for different measurement parameters a correlated signal with variable amplitude is modulated. Method according to claim 2, characterized in that that noise functions with defined seed values in the generation the noise signal can be used so that correlations between different Errors in the computational error determination taken into account can be. Method according to claim 2, characterized in that that the noise modulation is selectively switched on and / or off. Method according to claim 2, characterized in that that for analyzing the effects of correlated sources of error, So if between the error sources of two different output variables functional relationship exists, a series of error time of a first Output by use exactly identical seed values are reproduced exactly and with e.g. modulated on another sign or other amplitude of another output becomes. Method according to one of the preceding claims, characterized characterized in that an autocovariance analysis of the noise signal contribution at any intermediate point of the data processing routines determined program sequence is carried out, so that a computational error determination for all Intermediate processing sizes becomes feasible.